How can I subdivide a face which is next to a face that is already subdivided?
As these are ngons, you aren't able to use neither Loopcut, nor W > Subdivide. So you can do that in 2 ways:


Select ngon's edge in the bottom and subdivide it. Use then J to connect vertices and split faces.





Press K to activate Knife Tool. By clicking LMB you mark places where vertice will be placed.